New collective effects in weakly and strongly coupled dusty plasmas have been found. For example, we have discovered linear and nonlinear dust acoustic waves (Planet. Space Sci. 38, 543, 1990 SCI=1101), the dust ion-acoustic wave (Phys. Scr. 45, 504, 1992-SCI=202; Phys. Scr. 45, 508, 1992; SCI=543), dust charge fluctuation induced dust acoustic wave damping (Phys. Rev. E 47, 3612, 1993-SCI=276), Shukla-Varma mode (PF B 5, 236, 1993-SCI=81), Mach cones in magnetized dusty plasmas (PRL 92, 095005, 2004 SCI=18), solitary potential structures (Planet Space Sci. 40, 973, 1992 SCI=121; Planet. Space Sci. 42, 221, 1994 SCI=73; PoP 3, 702, 1996 SCI=180; PoP 3, 2610, 1996-SCI=125; PoP 9, 1468, 2002-SCI=123; PLA 290, 173, 2001-SCI=85) and dust ion-acoustic shock (PRL 83, 1602, 1999; SCI=251; IEEE Trans. Plasma Sci. 30, 720, 2002-SCI=59), dust drift vortices (JGR 96, 21343, 1991; SCI=112), dispersion properties of a dusty plasma containing non-spherical rotating dust grains (PRL 84, 2626, 2000 SCI=42; PoP 7, 1044, 2000 SCI=87), gravitational radiation from dusty plasmas and supernovae (JETP Lett. 81, 135, 2005), envelope solitons and cavitons in complex plasmas (PRE 58, 6517, 1998 SCI=81; PRL 91, 075005, 2003; PoP 11, 584, 2004), the parametric instability of dust lattice waves in a turbulent plasma sheath (PRL 84, 5328, 2000 SCI=28; JETP 93, 301, 2001), and the wakefiield (PLA 203, 40, 1995-SCI=163; PoP 3, 1770, 1996-SCI=73) for charged dust grain attraction, while the parametric instability theory (PRL 84, 5328, 2000-SCI=28) contributes to the understanding of the observed "sublimation" transition of the plasma crystal from a solid to a gaslike state. Furthermore, the DAW, the DIA shock and the wakefiield have been observed in experiments. Recently, we have demonstrated acceleration of charged dust grains to hypervelocities in laboratory experiments (PRL 100, 155002, 2008 SCI=11). Our dusty plasma works (e.g. review papers in PoP 8, 1791, 2001-SCI=223 and PoP 10, 1619, 2003 SCI=62; NJP 5, 17, 2003 SCI=113; Rev. Mod. Phys. 81, 25-44 2009 SCI=141) have relevance to cosmic physics as well to low-temperature laboratory dusty discharges and to molecular clouds. Our textbook Introduction to Dusty Plasma Physics (P. K. Shukla and A. A. Mamun, IoP, 2002 SCI=947 via Google Scholar) summarizes an up-to-date knowledge of complex dusty plasmas, and is used worldwide for teaching dusty plasmas to undergraduate and graduate students.

II. Neutrino Plasma Physics:

A new whole subject has been opened by investigating nonlinear interactions (PLA 260, 107, 1996 SCI=64; PRL 83, 2703, 1999 SCI=52; Phys. Plasmas 7, 2166, 2000 SCI=18) between intense neutrinos and dense plasmas. Thus, we have solved many astrophysical problems (viz. the generation of magnetic fields in the Early Universe and on the surface of a neutron star, the generation of inhomogeneities in the Early Universe (PLA 233, 181, 1977; PRE 57, 2479, 1998, Phys. Plasmas 5, 2815, 1998, PLA 310, 182, 2003), supernova explosions, the origin of gamma ray bursts, etc in terms of the nonlinear neutrino plasma coupling involving collective interactions (Plasma Phys. Control. Fusion 41, A699, 1999). The collective neutrino plasma interaction work has been carried out in collaboration with professor Lennart Stenflo, professor Robert Bingham, professor Jose Tito Mendonca, late professor Hans Bethe and professor John Dawson.

III. Nonlinear Waves in Fluids and Geophysical Flows:

Various types of new nonlinear effects associated with gravity, internal and Rossby waves have been identified. New nonlinear structures in fluids and geophysical flows have been predicted. Reecent works deal with zonal flows and large scale structures in the planetary magentospheres and galaxies (Astron. Astrophys. 300, 933, 1995; PLA 307, 154, 2003; PLA 308, 280, 2003), as well as monster waves in oceans (PRL 97, 094501, 2006; JETP Lett. 84, 645, 2006). The latter works have outreached to public via media.

IV. Nonlinear Wave Phenomena in Astrophysical and Pair Plasmas:

Wave-wave and wave-particle interactions have been studied in order to understand microstructures in pulsar magnetospheres, the propagation of cosmic rays in the interstellar medium (ApJ Lett. 276, L49, 1984 SCI=9), and the orogin of cosmological magnetic fields (ApJ Lett. 599, L57, 2003 SCI=113 via Google Scholar). The focus was on stimulated scattering instabilities of radiation, the generation of magnetic fields, and the formation of non-envelope (PoP 2, 716, 1995 SCI=170) and envelope solitons (Astrophys. Space Sci. 117, 303, 1985 SCI=78), as well as Alfven vortices (ApJ Lett. 309, L63, 1986 SCI=82).

We have developed theories for numerous parametric processes (e.g. Z. Naturforsch. A 29, 1735, 1974 SCI=64; Phys. Fluids 18, 265, 1975 SCI=61; Nature 274, 874, 1978 SCI=24; Phys. Fluids 26, 87, 1983 SCI=61; JPP 31, 423, 1984 SCI=58; Phys. Plasmas 12, 084502, 2005 SCI=85) in uniform and nonuniform plasmas with and without an external magnetic field. Computer simulation studies have been carried out to demonstrate the excitation of density striations and temperature filaments by the combined action of the ponderomotive force and electron Joule heating nonlinearity in plasmas. Applications to laser-plasma interactions, ionospheric modification and laboratory experiments involving high-frequency heater and microwaves have been considered. The results also have applications in planetary magnetospheres and in astrophysics.

We have presented theories for the envelope solitons (PRL 36, 968, 1976 SCI=15; PF 20, 1286, 1977 SCI=65; Plasma Phys. 19, 889, 1977 SCI=61; PRA 30, 2110, 1984 SCI=70; PF 28, 1576, 1985 SCI=60), nonenvelope solitons (J. Math. Phys. 19, 2506, 1978 SCI=87; Phys. Fluids 23, 2146, 1980 SCI=70; JPP 28, 125, 1982 SCI=65; JPP 29, 409, 1983 SCI=73; GRL 22, 2709, 1995 SCI=185), double layers (PF 29, 3214, 1986 SCI=69), and vortices (GRL 22, 671, 1995 SCI=68). The results have been applied to the understanding of nonlinear wave phenomena in space and laboratory plasmas (e.g. our review article Space Sci. Rev. 92, 423, 2000 SCI=199). Recently, we have presented theories (PoP 6, 1677, 1999; ibid. 6, 4120, 1999) for nonlinearly modulated dispersive Alfv\'en waves which are observed in the Earth's ionosphere/magnetosphere as well as in the solar corona. Our most recent works (PRL 84, 4373, 2000 SCI=31; GRL 27, 89, 2000; PRL 90, 08502, 2003 SCI=42; PRL 90, 135001, 2003; JETP Lett 77, 647, 2003; GRL 31, doi: 10.1029/2003GL018047, 2004 ) provide nonlinear models for coherent electric field structures in the magnetosphere as well as auroral density cavities and 3D ion holes that are observed by POLAR, FREJA, and FAST spacecrafts. More recently (PRL 90, 085002, 2003), we have presented evidence (as detected by the CLUSTER spacecraft) of slow magnetosonic solitons at the magnetopause boundary layers, and provided a theoretical nonlinear model which is in excellent agreement with observations. We are also carrying out computer simulations of the formation of ions holes and their head-on collisions in association with the generation of fast electrons which drive Langmuir waves. The latter, in turn, get trapped in ion holes (PRL 92, 095006, 2004). The dynamics of electron holes in the presence of ion motion has also been studied by means of simulations (PRL 93, 45001, 2004). Our results on electron and ion holes are summarized in a review article (Phys. Reports 422, 225-290, 2006 SCI=49). We have also developed a new nonlinear theory for magnetic reconnection mediated by lower-hybrid phase space vortices (PRL 93, 015002, 2004), as well as for whistler spheromaks (PRL 99, 205005, 2007).

Here, various kinds of new relativistic nonlinear effects in plasmas (e.g. Phys. Reports 138, 1-149, 1986-SCI=251) are shown to exist. The focus is on the localization of high-power laser pulses (PRA 16, 1591, 1978 SCI=41; Phys. Fluids 27, 327, 1984 SCI=49; PRL 94, 065002, 2005), pair production by intense laser beams (PRA 46, 6608, 1992; SCI=113), and excitation of intense wakefields that are relevant for plasma based charged particle acceleration. This work has applications to the acceleration of charged particles in space and astrophysical plasmas. Our review article (PPCF 46, R1-R23, 2004-SCI=113) summrizes the present status of relativsitic engineering involving intense laser beams.

VIII. Nonlinear Convective Motion in Plasmas:

We have presented a self-consistent theory (PRA 23, 321, 1981 SCI=47) for the excitation of convective cells/zonal or sheared flows by drift waves in nonuniform magnetoplasmas. Zonal flows act as barrier for cross-field plasma particle transport. Detailed studies of linear and nonlinear convective cells and magnetostatic modes/magnetic zonal flows appear in our review article (Phys. Reports 105, 227-328, 1984 SCI=78 via The SAO/NASA Astrophysics Data System (ads) Server/Harvard). The calculation of thermal and non-thermal test particle cross-field transport has been carried out. Our results are applied to the understanding of anomalous transport in space and laboratory plasmas. Recently, we have developed a quasi-particle approach to the modulational instability of drift waves coupled with zonal flows (PRL 94, 165002, 2005; PRL 99, 205006, 2007), which are observed in the Earth's magnetosphere by the Cluster satellites.

A calculation of cross-field diffusion and the a.c. conductivity of a turbulent plasma has been done. Model nonlinear equations for the study of low-frequency (drift-Alfv'en, kink, tearing, etc.) turbulence in magnetized plasmas have been derived. New instabilities in nonuniform magnetoplasmas were found. In the nonlinear analyses, we have established cascading rules, self-organization, and chaos. Specifically, we have reported (e.g. PRL 41, 1656, 1978; Phys. Rev. A 34, 1582, 1986; Geophys. Res. Lett. 22, 671, 1995 SCI=68; Phys. Plasmas 5, 616, 1998) the existence of various types of vortices, which appear frequently in in the Earth's ionosphere, magnetosphere, and extraterrestrial environment. Also studied are the properties of multiscale electromagnetic tubulence based on the Hall-MHD equations (PRL 102, 045004, 2009 SCI=18). Furthermore, we have reported (Nature 463, 825-828, 2005 SCI=56) the discovery by the Cluster satellites of short scale (150 kilometers across) drift-kinetic Alfven vortices in the Earth's magnetospheric cusp region, via which the solar wind is transported in the near earth environments. Such an study is relevant for understanding the origin of aurora and space weather.

X. Dense Quantum Plasmas:

We are investigating collective processes in dense quantum plasmas (e.g. Nature Phys. 5, 92-93, 2009 SCI=36; Phys. Lett. A 352, 242, 2006 SCI=72; Phys. Lett. A 355, 378, 2006 SCI=70; PoP 13, 022313, 2006 SCI=62; Phys. Usp. 53, 51-76, 2010 SCI=60 via Google Scholar; Rev. Mod. Phys. 83, 885-906, 2011 SCI=2). We have demonstrated the existence of i) dark solitons and vortices (PRL 96, 245001, 2006 SCI=118; NJP 9, 98, 2007 SCI=10), ii) novel fluid turbulence aspects (PRL 99, 125002, 2007 SCI=55; NJP 10, 083007, 2008 SCI=10), iii) trapping of light into electron holes (PRL 99, 096401, 2007 SCI=52), iv) and a quantum diode (PRL 100, 036801, 2008) at quantum scales. The results are relevant to microelectronics and nanotechnologies at nanoscales (e.g. semiconductors, nanowires, nano electron tubes, quantum diodes), as well as to compact astrophysical objects (dense neutron stars/magnetars, massive white dwarfs, supernovae) and to the next generation intense laser-solid density plasma interaction experiments.

We have investigated modulational and filamentation instabilities as the formation of dark, grey, and bright solitons in optical fibers accounting for the Kerr and non-stationary nonlinearities on an equal footing. The roles of saturable nonlinearity and spectral broadning on the filamentaion instability of optical pulses have been examined. The results have been published in Optics Lett. 11, 171-173 (1986) SCI=42; Phys. Scr. T98, 12-17 (2002), Optics Lett. 30, 2548-2550 (2005), etc.

We are investigating the modulational instability (Eur. Phys. J:B 46, 381-384, 2005; Eur. Phys. J: B 50, 321-325, 2006) and collapse of Bose-Einstein condensates (BECs) in multi-space dimensions. We have reported on the Newtonian dynamics of trapped bright solitons in a nonuniform potential that confines BECs. A new method for filtering and controlling solitons in a nonuniform BEC potential has been presented (JETP 80, 609-613, 2004). We have also investigated the dynamics of BECs within the framework of a wave-kinetic description (PLA 340, 355-360, 2005; JETP 101, 942-948, 2005).

We are exploring new nonlinear interactions between intense photons and a photon gas, taking into account the vacuum nonlinearity causedby QED effect. We observe interesting non-stationary phenomena of photonic pulses and the formation of light bullets and wedges. The results have relevance to astrophysical settings (e.g. magnetars) and forthcoming intense laser-matter experiments. Preliminary results have been published in PRL 92, 073601 (2004) SCI=17; PRL 98, 125001 (2007) SCI=27; JETP Lett. 79, 208-212 (2004); PoP 11, 3767-3778 (2004); PLA 330, 131-136 (2004). Our review article on nonlinear collective effects in photon-photon and photon-plasma interactions appears in Rev. Mod. Phys. 78, 591-640 (2006) [SCI=326].

We are investigating nonlinear properties of metamaterials (media with negative index of refraction). We have presented studies of the modulational instability (PRE 72, 016626, 2005 SCI=49) and localization of electromagnetic waves (PLA 341, 231-234, 2005) in metamaterials. The work has relevance to photonic crystals and light bending from a rotating black hole.

Professor Shukla's multifaceted research works have public outreach through media. Five ground breaking
recent works have caught media's attention. First, he and his European colleagues discovered (Sundqvist, Krasnoselskikh, Shukla et al, Nature 436, 825-828, 2005) the drift-kinetic Alfven vortices of tens of kilometers across in data from the Cluster mission at the cusp of the Earth's magnetosphere. This paper received wide publicity through press releases (e.g. Nature News on 10 August 2005 "Magnetospheric Physics: Turbulence on a Small Scale; Nature Physics News on 11 August 2005 "New Twist on Turbulence"; ESA News on 10 August 2005 "From Macro to Micro Turbulence"), through Physicsworld.com on 10 August 2005 "Cluster Makes Turbulent Breakthrough", and through German news papers and internet (e. g. Die Zeit on 10 August 2005 "Kleine Wirbel durch den Schutzschiled"; Deutschlandfunk on 10 August 2005 "Himmlische Strudel"; Wissenschaft.de on 11 August 2005 "Wie der Sonnenwind den Schutzschild der Erde durcheinander wirbelt", etc.) The observations were comapred with theory (Shukla, Yu & Stenflo, Electromagnetic drift vortices, Phys. Rev. A 34, 1582, 1986) and simulations, and showed striking agreement. Second, his pioneering work on instability and evolution of nonlinearly interacting water waves (Shukla et al, Phys. Rev. Lett. 97, 094501, 2006 SCI=48 via Google Scholar) had a wide coverage in Physical Review Focus on 1 September 2006 "Waves of Destruction"; Science News "Dashing rouges freak ocean waves pose threat to ships, deep-sea oil platforms" (Vol. 170, p. 328, 18 November 2006); on line Rheinische Post on line 20 September 2006 "Ausage fuer Monsterwellen?"; BBV-NET 20 September 2006 "Neue Theorie zum Verhalten des Wassers auf hoher see-Wie Monsterwellen etstehen" ; Informationdienst Wissenschaft 12 September 2006 "Wie die Mosnterwelle entsteht: RUB-Physiker entwickeln neue Theorie zum Verhalten des Wassers"; PhysOrg.com 13 Sept. 2006 "New theory (and old equations) may explain causes of ship-shinking freak waves"; article online forskning.se 14 Aug. 2006 "Sma vagsvall ger ovantade monstervagor"; Svobodanews.ru 18 September 2006 "Giant ocean waves obey the Schroedinger equation"; on line prophysik.de 13 Sept. 2006 "Wie die Mosnterwelle entsteht"; as well as in many magzines (Springer Geowissenschaften 13 Sept. 2006 "Wie entsteht eine Monsterwelle") and news papers (e.g. Die Zeit, "Vierzig Meter Wasser", Nr. 35, p. 33, 23 August 2007) in Europe. Third, a recent work (R. Trines et al, Phys. Rev. Lett. 99, 255502, 2007) reported spontaneous generation of self-organized solitary structures at Earth's magnetopause, which was in ESA Space and Technolgy News "Solitons found in the Magnetopause" on 7 March 2008, as well as in ESA Space Science News "Solitary Waves in Translation" on 7 March 2008. This PRL 2007 paper reports, for the first time, a direct comparison of multi-spacecraft Cluster observations and matched numerical modelling of drift wave-zonal flow solitons, unambiguously showing that these structures penetrate down the plasma density gradient in the magnetospheric boarder. Fourth, our work (Shaikh & Shukla, Phys. Rev. Lett. 102, 045002, 2009) dealing with 3D simulations of fluctuation spectra in the Hall-MHD plasma successfully explains the high-frequency electromagnetic wave observations from the solar wind plasma. This work has received a wide range of coverage through different media (e.g. Phys. Org, AlphaGalileo.Org, ProPhysik, InterestAlert, ScainceDaily, AstroNews German, RUB News (Innovation Report), German News through idw-online.de, UAH News). Fifth, the dreded giant freak waves, which can appear on the open sea out of nowhere, can now be explained and predicted with the help of a new statistical model for nonlinear, interacting water waves in our computer simulations (Eliasson & Shukla, Phys. Rev. Lett. 105, 014501, 2010). The statistical nonlinear model explains how the dispersive water-wave system evolves due to nonlinear effects in the wave-wave interaction and, above all, how it temporarily stabilizes itself through the broadening of the wave spectrum. There is a wide coverage of the present work in media and news papers (e.g. Speigel.Online, Scientific Computing, www.innovations-report.de, Deutschflüster, Metropoleruhr, ShortNews, TT.Com, Finanzteff, rp-online, Yahoo Nachrich-Deutschere Depeschendienst, Service & News, dradio.de, Welt-Sonntag, Rheinsische Post, Moneyspiegel.de, Kölnische Rundaschau, http://www.fona.de/de, idw (Ruhr--Universität Bochum), derstandard.at, WELT-ONLINE, ScineXXX, www.pro-physiik.de, www.scienZZ.de, Aqua Globe Magzine, www.nachrichten.de, www.wetsand.com/greenroom, http://pressetext.de/news.